Self-avoiding walks subject to a force

TL;DR

This paper proves that the free energy dependence on force is identical whether applied at the last vertex or the top plane in self-avoiding walks, with implications for numerical analysis and convergence rates.

Contribution

It establishes a theoretical equivalence in free energy behavior under different force application points for self-avoiding walks.

Findings

Force dependence of free energy is identical at last vertex and top plane.

Results are relevant to numerical simulations and convergence analysis.

Provides theoretical foundation for force application effects in self-avoiding walks.

Abstract

We prove some theorems about self-avoiding walks attached to an impenetrable surface (i.e. positive walks) and subject to a force. Specifically we show the force dependence of the free energy is identical when the force is applied at the last vertex or at the top (confining) plane. We discuss the relevance of this result to numerical results and to a recent result about convergence rates when the walk is being pushed towards the surface.